Practical application of lithium (Li) metal anodes has been hindered by Li dendrite growth, which renders a low Coulombic efficiency and short lifespan of working Li metal batteries. A stable solid electrolyte interphase (SEI) is crucial in suppressing the formation of Li dendrites. Herein the local stress and deformation evolvement status of a SEI layer during Li electrodeposition are investigated through a quantitative electrochemical–mechanical model based on a finite element method. Furthermore, the impacts of structural uniformity and mechanical strength on the stability of the SEI under different working conditions are investigated. Improving the structural uniformity of SEI is the most effective way to enhance the stability of SEI, which regulates ion transportation. In addition, pursuing extremely high mechanical strength is shown to be pointless, and a moderate elastic modulus of 3.0 GPa is suggested. This work affords an insight into the rational design of stable SEI layers and sheds light on a possible pathway toward practical applications of Li metal anodes. The failure mechanism of a solid electrolyte interphase (SEI) is systematically studied based on a quantitative electrochemical–mechanical model. How the SEI regulates Li dendrite growth, when SEI fails, and what is the key determinant for stable SEIs are discussed in detail. This work affords theoretical guidance for the design of stable SEIs.